My guess would be the map sensor? If you pop your cover off the top of your engine it is near the egr inlet tube on the manifold. It normally gets caked in soot these are pictures of the egr diffuser tube that go into your intake, the map sensor is located nearby so you can imagine how it will...
Hm, it may be losing prime. I don’t think mine runs that long. You can try the same procedure 3 times then attempt to start. Have you serviced the fuel filter? Are any codes present?
Turn the key to run, but not all the way to engage the starter and listen carefully near the bed to hear the pump turn on, the pump should run for 5-10 seconds at a whine sound.
Sounds like something with the lift pump is acting up. When you run below half a tank, the hot fuel coming back from the return line dumps on top of the pump causing it to over heat.